Description: Deduction adding an antecedent to both sides of a logical equivalence. (Contributed by NM, 11-May-1993)
Ref | Expression | ||
---|---|---|---|
Hypothesis | imbid.1 | ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) | |
Assertion | imbi2d | ⊢ ( 𝜑 → ( ( 𝜃 → 𝜓 ) ↔ ( 𝜃 → 𝜒 ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imbid.1 | ⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) | |
2 | 1 | a1d | ⊢ ( 𝜑 → ( 𝜃 → ( 𝜓 ↔ 𝜒 ) ) ) |
3 | 2 | pm5.74d | ⊢ ( 𝜑 → ( ( 𝜃 → 𝜓 ) ↔ ( 𝜃 → 𝜒 ) ) ) |